Multiplexing regulated traffic streams: design and performance

The main network solutions for supporting QoS rely on traf- fic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only ag- gregates regulated). The regulator proposed could be based on the (dual) leaky-bucket mechanism. This explains the interest in network element per- formance (loss, delay) for leaky-bucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sources’ traffic, we derive approxi- mations for both small and large buffers. Importantly, for small (large) buffers the short-term (long-term) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient tech- niques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applica- ble under more general conditions, are based on optimal resource (band- width and buffer) partitioning. They can also be directly applied to set GPS (Generalized Processor Sharing) weights and buffer thresholds in a shared resource system

Performance analysis of an asynchronous transfer mode multiplexer with Markov modulated inputs

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 1993.Thesis (Ph.D.) -- Bilkent Iniversity, 1993.Includes bibliographical references leaves 108-113.Asynchronous Transfer Mode (ATM) networks have inputs which consist of superpositions of correlated cell streams. Markov modulated processes are commonly used to characterize this correlation. The first step through gaining an analytical insight in the performance issues of an ATM network is the analysis of a single channel. One objective of this study is the performance analysis of an ATM multiplexer whose input is a Markov modulated periodic arrival process. Based on the transient behavior of the nD/D/1 queue, we present an approximate method to compute the queue length distribution accurately. The method reduces to the solution of a linear differential equation with variable coefficients. Another general traffic model is the Markov Modulated Poisson Process (MMPP). We employ Pade approximations in transform domain for the deterministic service time distribution in an M MPP/D/1 queue so as to compute the distribution of the buffer occupancy. For both models, we also provide algorithms for analysis in the case of finite queue capacities and for computation of effective bandwidth.Akar, NailPh.D

Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the approximation may not inherit these properties automatically.We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials and rational functions that preserve nonnegativity.(trigonometric) polynomials;rational functions;semidefinite programming;regression;(Chebyshev) approximation

Compact Markov-modulated models for multiclass trace fitting

Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes

Analysis of generic discrete-time buffer models with irregular packet arrival patterns

De kwaliteit van de multimediadiensten die worden aangeboden over de huidige breedband-communicatienetwerken, wordt in hoge mate bepaald door de performantie van de buffers die zich in de diverse netwerkele-menten (zoals schakelknooppunten, routers, modems, toegangsmultiplexers, netwerkinter- faces, ...) bevinden. In dit proefschrift bestuderen we de performantie van een dergelijke buffer met behulp van een geschikt stochastisch discrete-tijd wachtlijnmodel, waarbij we het geval van meerdere uitgangskanalen en (niet noodzakelijk identieke) pakketbronnen beschouwen, en de pakkettransmissietijden in eerste instantie één slot bedragen. De grillige, of gecorreleerde, aard van een pakketstroom die door een bron wordt gegenereerd, wordt gekarakteriseerd aan de hand van een algemeen D-BMAP (discrete-batch Markovian arrival process), wat een generiek kader creëert voor het beschrijven van een superpositie van dergelijke informatiestromen. In een later stadium breiden we onze studie uit tot het geval van transmissietijden met een algemene verdeling, waarbij we ons beperken tot een buffer met één enkel uitgangskanaal. De analyse van deze wachtlijnmodellen gebeurt hoofdzakelijk aan de hand van een particuliere wiskundig-analytische aanpak waarbij uitvoerig gebruik gemaakt wordt van probabiliteitsgenererende functies, die er toe leidt dat de diverse performantiematen (min of meer expliciet) kunnen worden uitgedrukt als functie van de systeemparameters. Dit resul-teert op zijn beurt in efficiënte en accurate berekeningsalgoritmen voor deze grootheden, die op relatief eenvoudige wijze geïmplementeerd kunnen worden

COMPUTER NETWORK ANALYSIS AND OPTIMISATION

This thesis presents a study and analysis of the major influences on network cost and their related performance. New methods have been devised to find solutions to network optimisation problems particular to the AT&T ISTEL networks in Europe and these are presented together with examples of their successful commercial application. Network performance is seen by the user in terms of network availability and traffic delay times. The network performance is influenced by many parameters, the dominating influences typically being the number of users accessing the network, the type of traffic demands they place upon it and the particular network configuration itself. The number of possible network configurations available to a network designer is vast if the full range of currently available equipment is taken into account. The aim of this research has been to assist in the selection of most suitable network designs for optimum performance and cost. This thesis looks at the current differing network technologies, their performance characteristics and the issues pertinent to any network design and optimisation procedures. A distinction is made between the network equipment providing user 'access' and that which constitutes the cross country, or *core\ data transport medium. This partitioning of the problem is exploited with the analysis concentrating on each section separately. The access side of the AT&T ISTEL - UK network is used as a basis for an analysis of the general access network. The aim is to allow network providers to analyse the root cause of excessive delay problems and find where small adjustments to access configurations might lead to real performance improvements from a user point of view. A method is developed to allow statistical estimates of performance and quality of service for typical access network configurations. From this a general method for the optimisation of cost expenditure and performance improvement is proposed. The optimisation of both circuit switched and packet switched computer networks is shown to be difficult and is normally tackled by the use of complex procedures on mainframe computers. The new work carried out in this study takes a fresh look at the basic properties of networks in order to develop a new heuristic method for the design and optimisation of circuit switched core networks on a personal computer platform. A fully functional design system was developed that implements time division multiplexed core network design. The system uses both a new heuristic method for improving the quality of the designs and a new 'speed up' algorithm for reducing times to find feasible routes, thereby dramatically improving overall design times. The completed system has since been used extensively to assist in the design of commercial networks across Europe.AT&T ISTEL Ltd., Redditch, Englan

Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the approximation may not inherit these properties automatically.We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials and rational functions that preserve nonnegativity.

Construction of new rational approximants based on transformational high dimensional model representation and their applications on LSI systems

Oransal yaklaştırım yöntemlerinin, tek veya çok değişkenli fonksiyonlardaki doğrusal olmama durumlarının veya tekilliklerin üstesinden gelmede kullanılan en etkin ve oluşturulması en kolay yaklaştırım yöntemleri olduğu söylenebilir. Bu yöntemler, çok değişkenli, doğrusal öteleme altında değişmeyen sistemlerdeki (ing: Multidimensional Linear Shift Invariant-LSI recursive systems) model indirgeme uygulamalarında, çok düzeyli birleştiricilerdeki (ing: multiplexer models) paket kayıp olasılıklarının hesaplanmasında ve üç boyutlu şekilleri yeniden oluşturmada (ing: shape reconstruction) kullanılırlar. Bu çalışmada, çok değişkenli, yeni bir oransal yaklaştırım yöntemi geliştirilmiş, yöntemin özellikleri, günümüzde oransal yaklaştırım yöntemlerinin en başında gelen Padé yaklaştırım yöntemi ile karşılaştırmalar yaparak tartışılmıştır. Burada sunulan oransal yaklaştırım çizemi, YBMG’nde (Yüksek Boyutlu Model Gösterilimi) yapılan kesmelere dayanır. YBMG, analitik yapısı bilinen çok değişkenli fonksiyonları daha az değişken içeren bir takım fonksiyonların toplamı olarak yaklaştırmaya dayanan ve son 15 yılda geliştirilen bir yaklaştırım yöntemidir. Çalışmada, yaklaştırımın niteliğini arttırmak amacı ile yöntemin yapısına bir takım esneklikler katılmıştır. YBMG, asıl fonksiyon yerine fonksiyonun birinci derece dönüşüm altındaki görüntüsüne uygulanmıştır. Bu da bize yaklaştırıma fazladan esneklik katabilme olanağını vermiştir. YBMG aracılığı ile elde edilen bu yeni yaklaştırım yönteminin fiziksel problemlerdeki davranışını gözlemlemek amacı ile, yöntem doğrusal öteleme altında değişmeyen, çok değişkenli sistemlere (LSI) uygulanmıştır. Bunun dışında, tek değişkenli bir yapay fonksiyon örneği de, yöntemin tek değişkenli fonksiyonlardaki etkinliğini incelemek için verilmiştir. Sonuçlar, tek veya çok değişkenli bir fonksiyonu Padé oransal yaklaştırım yöntemine göre daha geniş bir aralıkta yaklaştırabildiğimizi göstermektedir. Anahtar Kelimeler: Yüksek boyutlu model gösterilimi, oransal yaklaştırım, çok değişkenli analiz.There are plenty of methods to approximate a multivariate function arising from different concepts. Some of them are based on the truncation of infinite series like Taylor series or orthogonal expansions. These do not explicitly reflect the singularities of the function to be approximated. One of the infinite series explicitly showing singularities is the Laurent series, which include finite or infinite simple fractions to represent polar singularities. Since any rational function can be uniquely represented by a Laurent series, it is common practice to use rational approximants for approximating the functions to explicitly reflect all polar singularities. Padé approximants are perhaps the most frequently used ones in this category. Functions having strong singularities like branch points or essential singularities need special attention and can be approximated by using more specific techniques. Rational approximation techniques are perhaps the leading and easiest ones used to handle nonlinearities or singularities in the approximation of univariate or multivariate functions in science and engineering. They can be used in model-reduction of multidimensional Linear Shift Invariant (LSI) recursive systems, computing packet loss probabilities in multiplexer models, and shape reconstruction. In this work, we construct a new multivariate rational approximation method and discuss its advantages and disadvantages by comparing with the Padé technique, which is at the moment the leading rational approximation technique. The rational approximation scheme proposed here is formulated by using HDMR (High Dimensional Model Representation) truncations. HDMR has been developed in the last 15 years to approximate multivariate functions by a sum of less variate functions. Here, we insert certain flexibilities into the approximation, in order to improve its quality. The most general class of this type of HDMR is called "Transformational High Dimensional Model Representation" (THDMR). In THDMR, the image of the original multivariate function is approximated by a sum of less variate functions. The coefficients of the transformation are considered as optimization parameters, which make the error of the method as small as possible. In this work, a first degree polynomial structure is used as THDMR's operator and the coefficients of this first degree transformation are assumed to be varying with independent variables. This is for giving flexibilities to the transformation and fixing them to approximate the HDMR expansion optimally. Although THDMR has a more general structure than we used here, we chose to work with the first degree polynomial structure for unique invertibility. Once an approximation for this first order polynomial structure constructed by HDMR method, the approximation for the original function can be obtained by inverting the polynomial structure. The rational structure of the method comes from this special choice of THDMR operator. The univariate and bivariate results are quite impressive and imply that we can approximate a multivariate function over a quite larger interval when compared with the Padé method. This is caused by the fact that these two methods involve different strategies of extracting information from the original function. In THDMR method, the integral of the original function is computed over a specified interval to extract information from it, while Padé approximation method uses the derivatives of the function in a specific point. So THDMR method approximates the function more uniformly compared with Padé approximation technique which exhibits a local character. Moreover, the quality of the approximation can be improved by changing the integration intervals in THDMR. An important defect of the rational approximation techniques is that they can produce some poles over the focused interval, although the original function has no singularity over the same interval at all. The singularity problem exists also in THDMR method. However, in THDMR, in order to obtain the rational approximant, certain integrals are needed to be computed and the location of the possible poles of the approximant can be altered by changing the interval of the integration. This facility of changing the locations of the poles with the integration interval makes the method attractive and efficient. In order to see the behavior of the method on physical problems, we have applied it on LSI systems to reduce the system. The transfer function of the LSI system has been approximated by THDMR and Padé methods. The results show that, the newly developed THDMR method can be used on LSI systems with high level approximation quality. Keywords: High dimensional model representation, rational approximation, multivariate analysis

Modelling of reliable service based operations support system (MORSBOSS)

Philosophiae Doctor - PhDThe underlying theme of this thesis is identification, classification, detection and prediction of cellular network faults using state of the art technologies, methods and algorithms